Data defines the model by dint of genetic programming, producing the best decile table.

Interpretation of Coefficient-free ModelsBruce Ratner, Ph.D.

The ordinary regression model is the thought of reference when beginners-through- advanced model builders, and model end-users (e.g., those who know all about understanding and implementing models, but cannot build one) hear the words “new kind of model.” Data analysts use the regression concept and its prominent characteristics when judiciously evaluating an alternative modeling technique. This is because the ordinary regression paradigm is the underpinning for the solution to the ubiquitous prediction problem. End-users with limited statistical background undoubtedly draw on their educated notions of the regression model before accepting a new technique. Model builders go back to their first steps of the statistical model-building paradigm. New modeling techniques are evaluated by the coefficients they produce. The coefficients are deemed essential because they are always used as a measure of rank-order importance of variables that drive a model, i.e., that put variables into their proper places in relation to each other in predicting and explaining a model. If the new coefficients impart comparable information to the prominent characteristic of the regression model – the regression coefficient – then the new technique passes the first line of acceptance. If not, the technique is summarily rejected. A quandary arises when a new modeling technique, like machine learning methods, produces models with no coefficients.

The primary purpose of this article is to present a method for calculating a quasi-regression coefficient, which provides a frame of reference for evaluating and using coefficient-free models. Secondarily, the quasi-regression coefficient serves as a trusty assumption-free alternative to the regression coefficient, which is based on an implicit and hardly-tested assumption necessary for reliable interpretation. Click here.

For more information about this article, call Bruce Ratner at 516.791.3544 or 1 800 DM STAT-1; or e-mail at br@dmstat1.com.